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The reason nobody has responded, it is because your requirements are fully ambiguous.
What exactly do you want to accomplish?
A circuit powered up from a 20 volt supply? That it should amplify a -10 to +10 mv signal how much? What is your source and its impedance? Is it DC or AC, and if so to what frequency? The 350 mA output is it the maximum load, or do you want the signal to become a constant current of 350 mA? Is it going to swing from 0 to 350 mA or -350 to +350 mA?
this circuits is useful for instrumentation.all of voltage is DC.As you said 20 V is power supply,we want to control voltage with a variable resistor that gives 350 mA.I have two challenge with this circuits first,negative output voltage,second a high current in output.like a voltage divider circuits that is very simple.
a simple schematic or draft of your idea would help.
-10mV ... +10mV is a small voltage. What precision/resolution/noise... do you need?
then 350mA (source and sink?)
Let´s say you need 10% precision, then you need a max source impedance of 10mV * 10% / 350mA = 2.8mOhms. Even a connector or a piece of wire could be worse.
How would you overcome on this? 4-wire connection with regulation loop?
Re: how to make positive and negative voltage and high current
I'm no expert, but I'll offer my limited knowledge, and the high current part is a relative idea to each person, but there are many ways to create negative voltages.
Simple ones I know of are using ICs like the 7660 - that can only provide a negative voltage from -1.2 to -12V. There are lots of other ones to select from on suppliers power/voltage regulation sections and component lists.
I think you can create a negative reference with just diodes and capacitors, if I remember well it appears as info related to rectifiers and AC/DC power supplies when they discuss half wave and full wave and so on, but don't take my word on it.
If you want to do it a more involved way, page 19 of the attached pdf has this schematic (Figure 21) for a: "Regulated DC-to-DC Converter", and there must be many ways to achieve the same thing with other ICs.
From what I know, high current (more than a little IC, a voltage regulator, or a 200mA 555 can provide) seems to come from using a transistor or MOSFET after or around the voltage providing device - the jpg with two "high current" schematics from the ST L78xx series shows a way to do that.
Hope the little I know helps. Good luck.
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And I forgot the obvious one which might be more practical for your needs: A dual polarity regulated power supply using a centre-tapped transformer... Here's a reliable looking schematic: **broken link removed**